silly argument about infinity

[bo198214]

Simple proof that 0 times infinity and infinity are the same:

We know k*infinity = infinity
Let k = 0
Therefore 0 * infinity = infinity



Split from "The number circle revisited" ~Keiji

[Nick]

That's a good point.

[Keiji]

>.>

Zero times infinity is zero, when I said k*infinity = infinity, I meant k*infinity = infinity where k != 0

[bo198214]

or another one:

-oo = oo
0 = oo + oo = oo

*gg*

[Nick]

0 can be used in math because it represents nothing, which can be represented in physical form; if it can represented in the real world, it must be represented in math so it can be used to predict real-life situations, or whatever it is your using math for.

Infinity cannot be used in math because it represents an abstract idea that cannot be put into physical form.

I know that there are numbers that cannot be put in the real world, like imaginary numbers, but the problem is that infinity is not only useless; but it collides with 0, which is something that MUST be in math. 0 and infinity can never end up both being used in math, which is why the number circle is fundamentally flawed.

I sorta typed that out real quick, so I was probably ambiguous and redundant. Make since?

[d.m.falk]

All numbers are abstract. It just depends on what value you place on them.

d.m.f.

[Nick]

Infinity is an idea, same as 0. 0 is merely a symbol that represents nothing, and infinity is just the opposite; the difference is that the two are not compatible in the same mathematics, and 0 is useful (whereas infinity is useless).

[houserichichi]

You're just playing with points at infinity. I question how one decides that 0 times infinity is zero...it's similar to the old 0^0 discussion we had a long time ago - there are two conflicting arguments. One is that infinity times anything is infinity and the other is that 0 times anything is zero. It may be convenient at times to choose one over the other (depending, say, on geometry or a particular algebraic problem), but analytically and algebraically this is an undefined operation just like 0^0. I think bo was alluding to it but he was taken too seriously Sneaky sneaky bo.

[Nick]

0 x oo is the same as saying "0 sets of oo", which is still 0.
oo x 0 is the same as saying "an infinite number of 0's", which is also still 0.

[houserichichi]

Your argument is vacuous. You're treating infinity as a real number and assigning properties to it that aren't logically sound. If one multiplies any number of zeros together then, logically, one would get zero. This holds for any real number of multiplications. Infinity is not a real number and, thus, the argument doesn't necessarily hold. To show evidence of the fact consider the four limits that one could produce:

lim (x->infinity) x*0 = 0
lim (x->infinity) 0*x = 0
lim (y->0) infinity*y = indeterminate
lim (y->0) y*infinity = indeterminate

All you're considering in your multiplication are the first two cases, not the latter two.

The first limit says that if you multiply together an arbitrary number of zeros and then increase that number up to infinitely many then you will still have zero. The second says the same thing but commuted.

The third says that if you have infinitely many things and multiply them together but each time multiply fewer and fewer of them you can't say how many you have in the end. The fourth says the same thing. In fact, it might not even be true that the third and fourth are of the same thing either, depending on the algebraic structure of whatever it is you're talking about.

(addendum: You also can't say that the first multiplication 0xoo is a multiplication of sets but the second multiplication oox0 is one of numbers. Those are two very different uses of the 'x' symbol.)

[blazes816]

k = 5
let k = -5

oooooo.

[Nick]

I didn't learn about limits yet. But, other than the "your argument is vacuous" thing, it sounds like your on my side?

[wendy]

The arguments about 0/0 = x, or 0 * infinity = x, that are presented here assume that you are talking about the same 1/0 or infinity.

You can sometimes reliably do this calculation. It does not always work though, especially with the horotopic infinities. Euclidean geometry relies on this particular calculation.

The thing is that you are on each instance of 0 or infinity, trying to invoke some very large W, for which 1/W is indistinguishable from zero. Sometimes, it can be reliably implied that W_1 = W_2 +k or that W_1/W_2 = k. If you can't show this elsewise, then the invoking of W_1 and W_2 as separate entities is like trying to say x = y.

Infinity is best treated as a double-unknown, ie oo stands for some algebraic variable which is in turn standing for an algebraic variable.